Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

EPR Steering Inequalities from Entropic Uncertainty Relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.Comment: 10 pages, 2 figure

Cranial sutures work collectively to distribute strain throughout the reptile skull

The skull is composed of many bones that come together at sutures. These sutures are important sites of growth, and as growth ceases some become fused while others remain patent. Their mechanical behaviour and how they interact with changing form and loadings to ensure balanced craniofacial development is still poorly understood. Early suture fusion often leads to disfiguring syndromes, thus is it imperative that we understand the function of sutures more clearly. By applying advanced engineering modelling techniques, we reveal for the first time that patent sutures generate a more widely distributed, high level of strain throughout the reptile skull. Without patent sutures, large regions of the skull are only subjected to infrequent low-level strains that could weaken the bone and result in abnormal development. Sutures are therefore not only sites of bone growth, but could also be essential for the modulation of strains necessary for normal growth and development in reptiles

Hormonal Regulation of Capillary Fenestrae in the Rat Adrenal Cortex: Quantitative Studies using Objective Lens Staging Scanning Electron Microscopy

High magnification studies of the fenestrated capillary endothelium in the zona fasciculata (ZF) of rat adrenal glands were performed using the objective lens stage of an analytical scanning electron microscope (SEM) equipped with a lanthanum hexaboride emitter (LaB6). Resolution of surface substructure of the luminal membrane obtained with specimens decorated with gold/palladium (Au/Pd) was compared with that observed in others sputter coated with tantalum (Ta). High magnification (50,000x) of the fenestrated endothelium demonstrates that tantalum coating of the cryofractured adrenals improves the substructural detail compared to that seen in Au/Pd decorated specimens. The procedures used in specimen preparation, metal deposition and secondary electron imaging (SEI) are described. Quality imaging achieved using the objective lens stage is a result of the elimination of the SE-III component derived from backscattered electrons. Rat adrenals exhibited uniformly patent capillaries. High magnification micrographs of capillary walls were randomly recorded in two morphometric studies of the fenestral content of capillaries in the rat adrenal cortex. Adrenocorticotropic hormone (ACTH), when administered to rats following dexamethasone (DEX) treatment, significantly reduced the fenestrae/μm2 of endothelial surface and increased the mean size of fenestrae. After hypophysectomy, the number of fenestrae/μm2 declined over 48 h; within 2 h after ACTH was given to rats hypophysectomized 48 hours earlier, the fenestrae/μm2 had increased two-fold. These studies indicate that ACTH plays an important role in modulating fenestral content of the capillary endothelium in the adrenal cortex

Inhibitory postsynaptic actions of taurine, GABA and other amino acids on motoneurons of the isolated frog spinal cord

The actions of glycine, GABA, α-alanine, β-alanine and taurine were studied by intracellular recordings from lumbar motoneurons of the isolated spinal cord of the frog. All amino acids tested produced a reduction in the amplitude of postsynaptic potentials, a blockade of the antidromic action potential and an increase of membrane conductance. Furthermore, membrane polarizations occurred, which were always in the same direction as the IPSP. All these effects indicate a postsynaptic inhibitory action of these amino acids. When the relative strength of different amino acids was compared, taurine had the strongest inhibitory potency, followed by β-alanine, α α-alanine, GABA and glycine. Topically applied strychnine and picrotoxin induced different changes of postsynaptic potentials, indicating that distinct inhibitory systems might be influenced by these two convulsants. Interactions with amino acids showed that picrotoxin selectively diminished the postsynaptic actions of GABA, while strychnine reduced the effects of taurine, glycine, α- and β-alanine. But differences in the susceptibility of these amino acid actions to strychnine could be detected: the action of taurine was more sensitively blocked by strychnine compared with glycine, α- and β-alanine. With regard to these results the importance of taurine and GABA as transmitters of postsynaptic inhibition on motoneurons in the spinal cord of the frog is discussed

Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras

We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.Comment: 9 page

Resolving the Surfaces of Extrasolar Planets With Secondary Eclipse Light Curves

We present a method that employs the secondary eclipse light curves of transiting extrasolar planets to probe the spatial variation of their thermal emission. This technique permits an observer to resolve the surface of the planet without the need to spatially resolve its central star. We evaluate the feasibility of this technique for the HD 209458 system [..]. We consider two representations of the planetary thermal emission; a simple model parameterized by a sinusoidal dependence on longitude and latitude, as well as the results of a three-dimensional dynamical simulation of the planetary atmosphere previously published by Cooper & Showman. We find that observations of the secondary eclipse light curve are most sensitive to a longitudinal offset in the geometric and photometric centroids of the hemisphere of the planet visible near opposition. To quantify this signal, we define a new parameter, the ``uniform time offset,'' which measures the time lag between the observed secondary eclipse and that predicted by a planet with a uniform surface flux distribution. We compare the predicted amplitude of this parameter for HD 209458 with the precision with which it could be measured with IRAC. We find that IRAC observations at 3.6um a single secondary eclipse should permit sufficient precision to confirm or reject the Cooper & Showman model of the surface flux distribution for this planet. We quantify the signal-to-noise ratio for this offset in the remaining IRAC bands (4.5um, 5.8um, and 8.0um), and find that a modest improvement in photometric precision (as might be realized through observations of several eclipse events) should permit a similarly robust detection.Comment: AASTeX 5.2, 24 pages, 5 figures, accepted for publication in ApJ; v2: clarifications, updated to version accepted by ApJ; v3: try to reduce spacin